منحنی بازده در برآورد مدل کلان غیر خطی

This paper estimates a sticky price macro model with US macro and term structure data using Bayesian methods. The model is solved by a nonlinear method. The posterior distribution of the parameters in the model is found to be bi-modal. The degree of nominal rigidity is high at one mode (“sticky price mode”) but is low at the other mode (“flexible price mode”). I find that the degree of nominal rigidity is important for identifying macro shocks that affect the yield curve. When prices are more flexible, a slowly varying inflation target of the central bank is the main driver of the overall level of the yield curve by changing long-run inflation expectations. In contrast, when prices are more sticky, a highly persistent markup shock is the main driver. The posterior probability of each mode is sensitive to the use of observed proxies for inflation expectations. Ignoring additional information from survey data on inflation expectations significantly reduces the posterior probability of the flexible price mode. Incorporating this additional information suggests that yield curve fluctuations can be better understood by focusing on the flexible price mode. Considering nonlinearities of the model solution also increases the posterior probability of the flexible price mode, although to a lesser degree than using survey data information.

Dynamic term structure models that use a few factors to explain changes in the shape of the entire yield curve are empirically successful.1 In these models, factors are typically extracted from a statistical decomposition of the yield curve. However, the economic interpretation of such statistical factors is not clear. Recent empirical studies on the macroeconomics of the term structure (e.g., Ang and Piazzesi, 2003, Bikbov and Chernov, 2010 and Diebold et al., 2006) show a close link between macroeconomic variables and bond prices. These studies augment statistical factors of the yield curve with macroeconomic variables. Despite the inclusion of macro variables, latent term structure factors without a clear economic interpretation still explain a significant portion of the variation of the yield curve. In this paper, I set up and estimate a New Keynesian dynamic stochastic general equilibrium (DSGE) model to explain the joint fluctuations of macroeconomic variables and the yield curve. In the model, four different shocks drive economic fluctuations. They are shocks to technology, firms' price markups, the inflation target of the central bank, and a transitory monetary policy shock. I do not add latent term structure factors that are orthogonal to macro shocks and instead try to maximize the explanatory power of macro factors. By linking the estimates of shocks with empirical counterparts of latent term structure factors, I provide an economic interpretation of these purely statistical factors. In addition, the DSGE framework can shed light on the kind of endogenous amplification channels that can account for how these macro shocks drive yield curve fluctuations. Such an explanation is not possible to explore in factor models of the yield curve augmented with observed macro variables. This paper uses a second-order approximate solution in the estimation of the DSGE model. There are two reasons for this approach. First, Fernàndez-Villaverde et al. (2006), An (2005), and Amisano and Tristani (2007) show that there are noticeable differences in the likelihood and parameter estimates across first-order and second-order solutions. These differences are large when data are highly persistent. Bond yields have this property (see Fig. 1). Therefore, one can expect nonlinearities to be important in the estimation with yield curve data. Second, the first-order accurate solution of a DSGE model ignores terms which can contribute to term premia. I propose a method to analytically evaluate conditional expectations of no-arbitrage conditions for bond yields, based on the stochastic discount factor given by a second-order solution of the DSGE model. This approach differs from Hördahl et al. (2008), Ravenna and Seppälä (2006), and Rudebusch and Swanson (2008) who use various approximations for bond yields on top of a higher-order approximation to the macro solution.Three main findings are obtained from this study. First, the posterior distribution of the parameters in the model is found to be bi-modal. Posterior probability is much higher for the mode with a high degree of nominal rigidity (“sticky price mode”) than the mode with a low degree of nominal rigidity (“flexible price mode”). However, the posterior probability of each mode is sensitive to the inclusion of observed proxies for inflation expectations from the survey of professional forecasters. Since the flexible price mode captures the time variation of survey data better than the sticky price mode, including this additional information substantially increases the posterior probability of the flexible price mode. Second, nominal rigidity is important in identifying the macro factors of the yield curve. When prices are more flexible, the low-frequency movements of inflation and the overall level of the yield curve are mostly driven by nominal disturbances. But if prices are sticky, real disturbances matter more. The degree of nominal rigidity also determines which shocks account for the slope of the yield curve. For instance, when nominal rigidity is low, markup shocks are the main drivers of the slope; whereas, when nominal rigidity is high, monetary policy shocks dominate. Third, the nonlinearities of the model solution are also important for assessing the posterior probability of each mode. Ignoring nonlinearities of inflation dynamics reduces the posterior probability of the flexible price mode, although to a lesser degree than using survey data information. This paper is related to the literature linking estimated macro shocks obtained from DSGE models with the yield curve. Evans and Marshall (2007) use empirical measures of macro shocks to identify economic determinants of the nominal treasury bond yields. They argue that the systematic component of monetary policy is important in linking macro shocks with the yield curve. This paper also finds the importance of the systematic response of the policy rate in describing the way macro shocks influence the yield curve. However, the way I identify macro shocks is different. In Evans and Marshall (2007), some shocks are obtained from using first-order conditions of a DSGE model at the calibrated parameter values, whereas other shocks are obtained from using identifying restrictions in structural vector autoregressions from other papers. Therefore, the internal consistency of these measures is not clear.2 In contrast, this paper imposes restrictions of a single DSGE model to identify all the macro shocks. Another closely related paper is Bekaert et al. (2010) who combine the log-linear solution of a stylized New Keynesian model with the log-normality of the approximate pricing kernel. Their interpretation that the time-varying inflation target of the central bank is the main factor that explains the parallel shifts in the yield curve is in line with this paper. However, their use of the log-linear solution of the macro model ignores the role of nonlinear terms in the model solution. More importantly, neither of these studies discusses the role of nominal rigidity in identifying macro shocks driving the yield curve, which is the main focus of this paper. Additional literature closely related to this paper explores term structure implications of New Keynesian DSGE models solved with nonlinear methods (Hördahl et al., 2008; Ravenna and Seppälä, 2006; Rudebusch and Swanson, 2008, etc.).3 After reviewing the results of various papers, Rudebusch and Swanson (2008) conclude that stylized New Keynesian models have a hard time matching the first and second moments of term premia without compromising macro implications. In line with this finding, the model-implied term premia of the DSGE model studied in this paper are too stable compared to what is obtained by a reduced-form benchmark model. The remainder of the paper is organized as follows. Section 2 describes the model economy and presents a second-order approximation to model's solution and proposes a new method to derive equilibrium bond yields based on the second-order approximation. Section 3 describes data and the econometric methodology. 4 and 5 discuss the estimation results, and Section 6 concludes.

This paper estimates a small-scale New Keynesian model to identify macroeconomic sources of the yield curve. Unlike empirical factor models of the yield curve, this paper assumes that macro shocks in the DSGE model can explain the joint behavior of macro and term structure variables. I solve the macro model with a second-order approximation to equilibrium conditions and propose new closed-form solutions of bond prices given the second-order approximation to the macro model. This paper finds that the estimated degree of nominal rigidity is important for identifying macro factors driving yield curve fluctuations. When the estimated nominal rigidity is low, the inflation target of the central bank drives persistent movements of inflation and shifts the entire yield curve, while markup shocks affect mainly shorter-term maturities. Accordingly, the level of the yield curve is determined by the time-varying inflation target of the central bank and the slope of the yield curve is driven by markup shocks. In contrast, markup shocks become highly persistent and drive low-frequency movements of inflation and bond yields when the estimated nominal rigidity is high. The posterior distribution of parameters is bi-modal in terms of the degree of nominal rigidity. While the posterior mass of the sticky price mode is higher, survey data on inflation expectations seem to be more consistent with the flexible price mode. In fact, when I use survey data measures of inflation expectations in the estimation of the linear model, the posterior probability of the flexible price mode becomes much higher. Hence, a broad set of data support the flexible mode more than the sticky price mode. To a lesser degree than the inclusion of survey data information in the estimation, ignoring nonlinearities of the model solution also reduces the posterior probability of the flexible price mode. These findings indicate that incorporating additional information from observed proxies for inflation expectations and the nonlinearities of the model solution can be important for identifying macro shocks driving yield curve fluctuations.